The entry level Trek mountain bike comes in a wide variety of sizes. The "extra small" ladies version would fit many ten year olds. Nothing especially "lady-like" about the bike, other than the compact size.
And, it does use standard wheels and tires, unlike many "youth" models. And, by adding a longe seatpost, and higher and longer stem in a year or two, it would probably give you two or three good years of service before moving to a larger size.
The "list" price is around $250, but many shops in my area use this model as their "promotional" bike, and often have it on sale for $199 or so. Far superior to any bike from a department store or discount store, plus the service you would expect from a Trek dealer.